Discussing overweight passengers is like discussing politics or religion around the Thanksgiving dinner table with family: generally not a good idea.
When I saw the picture above, though, I felt compelled to address the issue. The picture you see was allegedly taken by an American Airlines flight attendant. Since bins are open and people are standing up, it appears it was taken during boarding.
I think we can all agree that allowing a passenger to protrude halfway into the aisle is clearly a safety violation. I also think it is safe to assume that the passenger was re-seated before takeoff to a row with an open middle seat.
Most U.S. airlines, including United and American, will not charge passengers of size (POS) for an extra seat as long as there are other open seats on the plane. I support this policy because I see no reason to castigate a POS further, especially when obesity is not always wholly dependent on lifestyle choice.
The problem arises when a flight is full and an airline is left with the choice of letting a POS literally occupy 1.5-2 Economy seats by allowing the arm rest to stay up and squeezing the other passengers in the row or having to VDB or even IDB a passenger to accommodate the POS. In such cases, I think an airline must give the POS the choice of stepping off the flight and waiting for the next one with an extra seat or paying for an extra ticket, perhaps at a lower cost.
Some posit that airline seats are too small and POS have no other alternatives. I disagree. United offers Economy Plus and First Class on most mainline domestic flights and Economy Plus, Business, and First Class on most international flights. Furthermore, it is not like airlines can easily (or even not so easily) install couches or rotund lazy boy recliners in their planes. To mandate that airlines compromise and dismantle a well-planned seating arrangements to accommodate a tiny sliver of the flying public is no more reasonable than arguing that an airline must make half-size seats available to compact people and only charge half-price for them.
Another analogy might be passenger baggage. Are bigger passengers allowed a higher weight allowance on checked bag? Of course not. They pay the same price as others and must abide by the same weight limits. Why should it be any different with onboard seating?
In some cases, like the picture above, any airplane seat (short of Singapore's A380 suites) would likely be too small for the passenger. In such cases, I believe a carrier should reserve the right to refuse passage on the grounds of passenger safety--both for the POS and others.
Am I missing something? How do you propose airlines deal with POS? Unfortunately, it is a growing problem in America. No pun intended.